General conditions for limit summability of solutions of nonlinear elliptic equations with image-data Original Research Article

We consider the Dirichlet problem for nonlinear elliptic second-order equations in divergence form with an L1L1-right-hand side f. By the function f we define other function with the values which are equal to the integrals of the function |f||f| over the sets {|f|⩾s}{|f|⩾s}, s⩾0s⩾0. Under rather general integral conditions on the latter function we prove that the entropy solution of the problem under consideration belongs to some limit Lebesgue and Sobolev spaces.